Variational methods in application to crack problems

In the project we propose to extend variational and numerical methods to constrained problems in non-smooth domains, with application to crack problems. Following the general goals of the current grant period and based on results obtained up to now, we propose to continue and extend our research in the following main directions: 1. Inverse and shape optimization problems for constrained models in non-smooth domains, based on shape sensitivity analysis, velocity, and level-set methods, with application to problems for cracks, crack propagation, and identification of cracks. 2. Analysis of primal-dual, semi-smooth, and active-set strategies for constrained minimization problems with respect to convergence properties, regularization and smoothing methods, for variational inequalities and non-linear crack problems. 3. Numerical simulations of problems with cracks under different type of boundary conditions, complicated geometrical data, motion of cracks, and high-dimensional models.